CBSE BOARD X, asked by Anonymous, 1 year ago

The interior angles of a polygon are in AP .The smallest angle is 52° and common difference is 8°.Find the number of sides of the polygon.

Anonymous: C..(TT)

floradas13fdoxpeix: Here data is insufficient

floradas13fdoxpeix: a1=52

floradas13fdoxpeix: a2=a+d=52+8=60

floradas13fdoxpeix: a3=a+2d=52+16=68

floradas13fdoxpeix: Like that n no. Of sides can be found bcz polygon starts with minimum 3 sides and lasts upto n no. Of sides,therefore determining the no. Of sides is not possible without sufficient data

Answers

Answered by prince614710

Given smallest interior angle is 52°Common difference is 8°
Each of the interior angle increases by 8°
Hence exterior decreases by 8°
Exterior angle corresponding to 52° = 180° - 52° = 128

Next exterior angle = 128° - 8° = 120° and so on Hence the AP is 128°, 120°…

Sum of exterior angles of a polygon = 360°

That is 128° + 120° +… n terms = 360°

Sum of n terms of AP is
(n/2)[2a + (n –1)d]
Hence, 360° = (n/2)[2(128°) + (n – 1)(-8°)]

solve this equation to get the value of n ; that is the number of sides of the polygon.

thanks ☺️☺️☺️

Anonymous: Thnq :)

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